# Tagged Questions

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### A criterion for complete lattice.

Is there an infinite partially ordered set $(X,\le)$, in which for each $A\subseteq X$, either $\inf A$ or $\sup A$ exists but for some $A\subseteq X$ either $\inf A$ or $\sup A$ does not exist.
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### an infinite queue preserving equality.

Is there any well-ordered set $(A,\leq)$ such that: $(A,\leq^{-1})$ is well-ordered. $A$ is infinite. there's exactly one function $\theta:A\rightarrow \{0,1\}$ such that 1) for each $a < M$, ...
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Can someone help me to solve this problem. Are these Hasse diagrams lattices?
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### Confusion with the lattice formed by a partition

I was referring to this article here related to the formation of a complete lattice by the partitions of a set. The article has stated that the partitions not only form the lattice for themselves but ...
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### Confusion about the lattice formed by an equivalence relation

I am a beginner in this field. Actually, I am studying about equivalence relation. I found that the set of all equivalence relations possible on set A form a relation. If R1 and R2 are two ...
I have noticed a certain analogy between subgroups of a group $G$ and equivalence relations on a set $X$. I would like to know if there's an explanation for this analogy or a common generalization of ...